Mathematical Foundations of SupersymmetryEuropean Mathematical Society, 2011 - 287 σελίδες Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context. |
Περιεχόμενα
Z2Zgraded linear algebra | 1 |
Sheaves functors and the geometric point of view | 28 |
Supergeometry | 45 |
Differentiable supermanifolds | 54 |
The local structure of morphisms | 97 |
The Frobenius theorem | 103 |
Super Lie groups | 113 |
Actions of super Lie groups | 143 |
Supervarieties and superschemes | 173 |
Appendices with the assistance of Ivan Dimitrov | 231 |
Classification of finitedimensional irreducible modules | 244 |
More on representations of Lie superalgebras | 254 |
Fréchet superspaces | 269 |
284 | |
286 | |
Homogeneous spaces | 154 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A-module affine superschemes algebraic supergroup Berezinian Borel subalgebra bracket Cartan Chapter classical Lie superalgebras coordinates corresponding define Definition denote diagram differential elements equivalent example exists a unique fact finite finite-dimensional Fréchet space functions functor F functor of points GLmn global sections Hence Hopf superalgebra hSpec invertible irreducible isomorphic left-invariant Let F Let G Lie group Lie superalgebra Lie supergroup Lie(G line bundles linear manifold Math matrices maximal ideal module natural transformation nilpotent notation open affine open cover open sets open subset ordinary setting presheaf Proof properties Proposition reader representation root system salg seminorms SHCP sheaf morphism sheafification sheaves Spec subfunctors subgroup submanifold subspace super Lie algebra super Lie group super vector space superalgebra morphism superdomains supergeometry supergroup functor supergroup scheme supermanifold superspace supervariety surjective tangent space topological space V₁ vector fields